RESUMEN

The gravity-induced depth-dependent elastic properties of a granular half-space result in multiple dispersive surface modes and demand the consideration of material heterogeneity in metabarrier designs to suppress surface waves. Numerous locally resonant metabarrier configurations have been proposed in the literature to suppress Rayleigh surface waves in homogeneous media, with little focus on extending the designs to a heterogeneous half-space. In this work, a metabarrier comprising partially embedded rod-like resonators to suppress the fundamental dispersive surface wave modes in heterogeneous granular media known as first order PSV (PSV1; where P is the longitudinal mode and SV is the shear-vertical mode) and second order PSV (PSV2) is proposed. The unit-cell dispersion analysis, together with an extensive frequency-domain finite element analysis, reveals preferential hybridization of the PSV1 and PSV2 modes with the longitudinal and flexural resonances of the resonators, respectively. The presence of the cutoff frequency for the longitudinal-resonance hybridized mode facilitates straightforward suppression of the PSV1 mode, while PSV2 mode suppression is possible by tailoring the hybridized flexural resonance modes. These PSV1 and PSV2 bandgaps are realized experimentally in a granular testbed comprising glass beads by embedding 3D-printed resonator rods. Also explored are novel graded metabarriers capable of suppressing both PSV1 and PSV2 modes over a broad frequency range for potential applications in vibration control and seismic isolation.

RESUMEN

Locally resonant elastodynamic metasurfaces for suppressing surface waves have gained popularity in recent years, especially because of their potential in low-frequency applications such as seismic barriers. Their design strategy typically involves tailoring geometrical features of local resonators to attain a desired frequency bandgap through extensive dispersion analyses. In this paper, a systematic design methodology is presented to conceive these local resonators using topology optimization, where frequency bandgaps develop by matching multiple antiresonances with predefined target frequencies. The design approach modifies an individual resonator's response to unidirectional harmonic excitations in the in-plane and out-of-plane directions, mimicking the elliptical motion of surface waves. Once an arrangement of optimized resonators composes a locally resonant metasurface, frequency bandgaps appear around the designed antiresonance frequencies. Numerical investigations analyze three case studies, showing that longitudinal-like and flexural-like antiresonances lead to nonoverlapping bandgaps unless both antiresonance modes are combined to generate a single and wider bandgap. Experimental data demonstrate good agreement with the numerical results, validating the proposed design methodology as an effective tool to realize locally resonant metasurfaces by matching multiple antiresonances such that bandgaps generated as a result of in-plane and out-of-plane surface wave motion combine into wider bandgaps.

RESUMEN

Control of guided waves has applications across length scales ranging from surface acoustic wave devices to seismic barriers. Resonant elastodynamic metasurfaces present attractive means of guided wave control by generating frequency stop-bandgaps using local resonators. This work addresses the systematic design of these resonators using a density-based topology optimization formulated as an eigenfrequency matching problem that tailors antiresonance eigenfrequencies. The effectiveness of our systematic design methodology is presented in a case study, where topologically optimized resonators are shown to prevent the propagation of the S0 wave mode in an aluminum plate.

RESUMEN

Ultrasonic guided waves provide unique capabilities for the structural health monitoring of plate-like structures. They can detect and locate various types of material degradation through the interaction of shear-horizontal (SH) waves and Lamb waves with the material. Magnetostrictive transducers (MSTs) can be used to generate and receive both SH and Lamb waves and yet their characteristics have not been thoroughly studied, certainly not on par with piezoelectric transducers. A series of multiphysics simulations of the MST/plate system is conducted to investigate the characteristics of MSTs that affect guided wave generation and reception. The results are presented in the vein of showing the flexibility that MSTs provide for guided waves in a diverse range of applications. In addition to studying characteristics of the MST components (i.e., the magnetostrictive layer, meander electric coil, and biased magnetic field), single-sided and double-sided MSTs are compared for preferential wave mode generation. The wave mode control principle is based on the activation line for phase velocity dispersion curves, whose slope is the wavelength, which is dictated by the meander coil spacing. A double-sided MST with in-phase signals preferentially excites symmetric SH and Lamb modes, while a double-sided MST with out-of-phase signals preferentially excites antisymmetric SH and Lamb modes. All attempted single-mode actuations with double-sided MSTs were successful, with the SH3 mode actuated at 922 kHz in a 6-mm-thick plate being the highest frequency. Additionally, the results show that increasing the number of turns in the meander coil enhances the sensitivity of the MST as a receiver and substantially reduces the frequency bandwidth.

Asunto(s)

RESUMEN

Rayleigh waves are very useful for ultrasonic nondestructive evaluation of structural and mechanical components. Nonlinear Rayleigh waves have unique sensitivity to the early stages of material degradation because material nonlinearity causes distortion of the waveforms. The self-interaction of a sinusoidal waveform causes second harmonic generation, while the mutual interaction of waves creates disturbances at the sum and difference frequencies that can potentially be detected with minimal interaction with the nonlinearities in the sensing system. While the effect of surface roughness on attenuation and dispersion is well documented, its effects on the nonlinear aspects of Rayleigh wave propagation have not been investigated. Therefore, Rayleigh waves are sent along aluminum surfaces having small, but different, surface roughness values. The relative nonlinearity parameter increased significantly with surface roughness (average asperity heights 0.027-3.992 µm and Rayleigh wavelengths 0.29-1.9 mm). The relative nonlinearity parameter should be decreased by the presence of attenuation, but here it actually increased with roughness (which increases the attenuation). Thus, an attenuation-based correction was unsuccessful. Since the distortion from material nonlinearity and surface roughness occur over the same surface, it is necessary to make material nonlinearity measurements over surfaces having the same roughness or in the future develop a quantitative understanding of the roughness effect on wave distortion.

RESUMEN

The propagation of ultrasonic guided waves in cortical bone has potential to inform medical caregivers about the condition of the bone structure. However, as waveguides, human long bones such as the tibia are complex in terms of their material behavior and their geometric features. They exhibit anisotropic elasticity and internal damping. For the first time, wave propagation is modelled in the irregular hollow tibial cross-section, which varies along its long axis. Semi-analytical, frequency domain, and time domain finite element analyses providing complimentary information about long-range wave propagation characteristics in such a waveguide are applied to the mid-diaphyseal region of a human tibia. Simulating the guided waves generated by a contact transducer, the signals received in axial transmission indicate the consistent presence of low phase velocity non-dispersive propagating modes. The guided waves capable of traveling long distances have strong potential for diagnosis of fracture healing.

Asunto(s)

RESUMEN

A nonlinear ultrasonic method is proposed based on a group of newly discovered wave triplets where two primary codirectional shear-horizontal SH0 waves mix in a weakly nonlinear plate and generate a cumulative S0 Lamb wave at the sum frequency. Theoretical analyses show that any combination of two primary SH0 waves whose frequencies sum to the frequency at which the SH0 mode intersects the S0 Lamb wave mode results in an internally resonant secondary S0 Lamb wave. Moreover, the relationship between the frequency combination and the nonlinear Lamb wave generation efficiency is revealed, which guides further engineering applications. Finite element validations are carried out with the aid of a subtraction method for the nonlinear feature extraction. The cumulative effect of the generated S0 Lamb wave at the sum frequency as well as the influence of the frequency combinations on the nonlinear Lamb wave generation efficiency is confirmed. Experiments are performed to validate the proposed method as well as demonstrate its use for material characterization. The experiments require a gel filter to mitigate the influence of the undesired nonlinear sources. With the gel filter, the cumulative effect of the secondary S0 Lamb wave is verified and the corresponding slope is extracted and further used to characterize the material status of the fatigue samples. Results demonstrate the proposed method provides high sensitivity to early fatigue damage, which makes it promising for the further early damage detection applications.

RESUMEN

Lamb waves propagating within a waveguide often have similar frequency content. If there are multiple Lamb wave modes with the same frequency content, the wavenumber spectrum can be used to distinguish between them. As a result, the wavenumber spectrum is an important tool for determining the modal content of signals. In this paper, we propose a new method for measuring wavenumber spectra that uses an air-coupled transducer for reception and Snell's law instead of a fast-Fourier transform. The method employs an angular scan rather than a translational scan. The advantages and disadvantages of the method are discussed along with some suggestions for potential improvements. Finally, experimental results comparing the proposed method to a more conventional method, which used a PVDF transducer, demonstrate the feasibility of the proposed method.

RESUMEN

The Partial Wave Method is unique in that it establishes a foundation on which various elastodynamic guided waves can be compared. In this paper, the method is used to compare quasi-Rayleigh waves and Rayleigh waves, and investigate the eccentricities of the Partial Wave Method at phase velocities equal to the Rayleigh wave speed. The comparison results in the definition of two types of quasi-Rayleigh waves and an explanation for quasi-Rayleigh wave behavior reported in the literature at frequencies that do not satisfy Viktorov's quasi-Rayleigh wave condition. These conclusions are also verified by the superposition of A0 and S0 mode wave-structures calculated using the semi-analytical finite element method.

RESUMEN

Elevated temperature, gamma radiation, and geometric constraints inside dry storage casks for spent nuclear fuel represent a harsh environment for nondestructive inspection of the cask and require that the inspection be conducted with a robotic system. Electromagnetic acoustic transducers (EMATs) using non-contact ultrasonic transduction based on the Lorentz force to excite/receive ultrasonic waves are suited for use in the robotic inspection. Periodic permanent magnet EMATs that actuate/receive shear horizontal guided waves are developed for application to robotic nondestructive inspection of stress corrosion cracks in the heat affected zone of welds in stainless steel dry storage canisters. The EMAT's components are carefully selected in consideration of the inspection environment, and tested under elevated temperature and gamma radiation doses up to 177 °C and 5920 krad, respectively, to evaluate the performance of the EMATs under realistic environmental conditions. The effect of gamma radiation is minimal, but the EMAT's performance is affected by temperatures above 121 °C due to the low Curie temperature of the magnets. Different magnets are needed to operate at 177 °C. The EMAT's capability to detect notches is also evaluated from B-scan measurements on 304 stainless steel welded plate containing surface-breaking notches.

RESUMEN

Hypervelocity impact (HVI), ubiquitous in low Earth orbit with an impacting velocity in excess of 1 km/s, poses an immense threat to the safety of orbiting spacecraft. Upon penetration of the outer shielding layer of a typical two-layer shielding system, the shattered projectile, together with the jetted materials of the outer shielding material, subsequently impinge the inner shielding layer, to which pitting damage is introduced. The pitting damage includes numerous craters and cracks disorderedly scattered over a wide region. Targeting the quantitative evaluation of this sort of damage (multitudinous damage within a singular inspection region), a characterization strategy, associating linear with nonlinear features of guided ultrasonic waves, is developed. Linear-wise, changes in the signal features in the time domain (e.g., time-of-flight and energy dissipation) are extracted, for detecting gross damage whose characteristic dimensions are comparable to the wavelength of the probing wave; nonlinear-wise, changes in the signal features in the frequency domain (e.g., second harmonic generation), which are proven to be more sensitive than their linear counterparts to small-scale damage, are explored to characterize HVI-induced pitting damage scattered in the inner layer. A numerical simulation, supplemented with experimental validation, quantitatively reveals the accumulation of nonlinearity of the guided waves when the waves traverse the pitting damage, based on which linear and nonlinear damage indices are proposed. A path-based rapid imaging algorithm, in conjunction with the use of the developed linear and nonlinear indices, is developed, whereby the HVI-induced pitting damage is characterized in images in terms of the probability of occurrence.

RESUMEN

Guided waves in plate-like structures have been widely investigated for structural health monitoring. Lamb waves and shear horizontal (SH) waves, two commonly used types of waves in plates, provide different benefits for the detection of various types of defects and material degradation. However, there are few sensors that can detect both Lamb and SH waves and also resolve their modal content, namely the wavenumber-frequency spectrum. A sensor that can detect both waves is desirable to take full advantage of both types of waves in order to improve sensitivity to different discontinuity geometries. We demonstrate that polyvinylidene difluoride (PVDF) film provides the basis for a multi-element array sensor that detects both Lamb and SH waves and also measures their modal content, i.e., the wavenumber-frequency spectrum.

RESUMEN

Harsh environments and confined spaces require that nondestructive inspections be conducted with robotic systems. Ultrasonic guided waves are well suited for robotic systems because they can provide efficient volumetric coverage when inspecting for various types of damage, including cracks and corrosion. Shear horizontal guided waves are especially well suited for robotic inspection because they are sensitive to cracks oriented perpendicular or parallel to the wave propagation direction and can be generated with electromagnetic acoustic transducers (EMATs) and magnetostrictive transducers (MSTs). Both types of transducers are investigated for crack detection in a stainless steel plate. The MSTs require the robot to apply a compressive normal force that creates frictional force coupling. However, the coupling is observed to be very dependent upon surface roughness and surface debris. The EMATs are coupled through the Lorentz force and are thus noncontact, although they depend on the lift off between transducer and substrate. After comparing advantages and disadvantages of each transducer for robotic inspection the EMATs are selected for application to canisters that store used nuclear fuel.

RESUMEN

This article describes the use of the frequency domain finite element (FDFE) technique for guided wave mode selection in inhomogeneous waveguides. Problems with Rayleigh-Lamb and Shear-Horizontal mode excitation in isotropic homogeneous plates are first studied to demonstrate the application of the approach. Then, two specific cases of inhomogeneous waveguides are studied using FDFE. Finally, an example of guided wave mode selection for inspecting disbonds in composites is presented. Identification of sensitive and insensitive modes for defect inspection is demonstrated. As the discretization parameters affect the accuracy of the results obtained from FDFE, effect of spatial discretization and the length of the domain used for the spatial fast Fourier transform are studied. Some recommendations with regard to the choice of the above parameters are provided.

RESUMEN

The characteristics of Lamb waves, which are multimodal and dispersive, provide both challenges and opportunities for structural health monitoring (SHM). Methods for nondestructive testing with Lamb waves are well established. For example, mode content can be determined by moving a sensor to different positions and then transforming the spatial-temporal data into the wavenumber-frequency domain. This mode content information is very useful because at every frequency each mode has a unique wavestructure, which is largely responsible for its sensitivity to material damage. Furthermore, mode conversion occurs when the waves interact with damage, making mode content an excellent damage detection feature. However, in SHM, the transducers are typically at fixed locations and are immovable. Here, an affixed polyvinylidene fluoride (PVDF) multielement sensor is shown to provide these same capabilities. The PVDF sensor is bonded directly to the waveguide surface, conforms to curved surfaces, has low mass, low profile, low cost, and minimal influence on passing Lamb waves. While the mode receivability is dictated by the sensor being located on the surface of the waveguide, both symmetric and antisymmetric modes can be detected and group velocities measured.

RESUMEN

Harmonic generation from non-cumulative fundamental symmetric (S0) and antisymmetric (A0) modes in plate is studied from a numerical standpoint. The contribution to harmonic generation from material nonlinearity is shown to be larger than that from geometric nonlinearity. Also, increasing the magnitude of the higher order elastic constants increases the amplitude of second harmonics. Second harmonic generation from non-phase-matched modes illustrates that group velocity matching is not a necessary condition for harmonic generation. Additionally, harmonic generation from primary mode is continuous and once generated, higher harmonics propagate independently. Lastly, the phenomenon of mode-interaction to generate sum and difference frequencies is demonstrated.

RESUMEN

The nonlinear forcing terms for the wave equation in general curvilinear coordinates are derived based on an isotropic homogeneous weakly nonlinear elastic material. The expressions for the nonlinear part of the first Piola-Kirchhoff stress are specialized for axisymmetric torsional and longitudinal fundamental waves in a circular cylinder. The matrix characteristics of the nonlinear forcing terms and secondary mode wave structures are manipulated to analyze the higher harmonic generation due to the guided wave mode self-interactions and mutual interactions. It is proved that both torsional and longitudinal secondary wave fields can be cumulative by a specific type of guided wave mode interactions. A method for the selection of preferred fundamental excitations that generate strong cumulative higher harmonics is formulated, and described in detail for second harmonic generation. Nonlinear finite element simulations demonstrate second harmonic generation by T(0,3) and L(0,4) modes at the internal resonance points. A linear increase of the normalized modal amplitude ratio A2/A1(2) over the propagation distance is observed for both cases, which indicates that mode L(0,5) is effectively generated as a cumulative second harmonic. Counter numerical examples demonstrate that synchronism and sufficient power flux from the fundamental mode to the secondary mode must occur for the secondary wave field to be strongly cumulative.

Asunto(s)

RESUMEN

Ultrasonic guided wave inspection of structures containing adhesively bonded joints requires an understanding of the interaction of guided waves with geometric and material discontinuities or transitions in the waveguide. Such interactions result in mode conversion with energy being partitioned among the reflected and transmitted modes. The step transition between an aluminum layer and an aluminum-adhesive-aluminum multi-layer waveguide is analyzed as a model structure. Dispersion analysis enables assessment of (i) synchronism through dispersion curve overlap and (ii) wavestructure correlation. Mode-pairs in the multi-layer waveguide are defined relative to a prescribed mode in a single layer as being synchronized and having nearly perfect wavestructure matching. Only a limited number of mode-pairs exist, and each has a unique frequency range. A hybrid model based on semi-analytical finite elements and the normal mode expansion is implemented to assess mode conversion at a step transition in a waveguide. The model results indicate that synchronism and wavestructure matching is associated with energy transfer through the step transition, and that the energy of an incident wave mode in a single layer is transmitted almost entirely to the associated mode-pair, where one exists. This analysis guides the selection of incident modes that convert into transmitted modes and improve adhesive joint inspection with ultrasonic guided waves.

Asunto(s)

RESUMEN

Theoretical formulation for the problem of second harmonic guided waves in pipes is presented from the principles of continuum mechanics. The formulation is carried out in the reference configuration of the pipe with an emphasis on the correct use of the "Divergence" operator in the reference configuration. Second harmonic guided wave generation from axis-symmetric longitudinal guided wave modes is studied. A large radius asymptotic approximation for the wave structures in pipe is studied and an error estimate for the same is obtained. Comparison with the corresponding modes in a plate and the analogy to second harmonic guided wave generation in plates is presented.